3D Mandelbrot !

Wonder how a 3D Mandelbrot looks like?

http://www.skytopia.com/project/fractal/mandelbulb.html

Kabuki

2009-11-14 18:55:03 UTC

Post by Penang
Wonder how a 3D Mandelbrot looks like?
http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

Alan Browne

2009-11-15 00:17:56 UTC

Post by Penang
Wonder how a 3D Mandelbrot looks like?
http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

Cool, indeed. Here are more:

http://www.bugman123.com/Hypercomplex/index.html

I don't believe these satisfy the self-similar aspect of the Mandlebrot
set. For that matter, does such exist in nature?

David Makin

2009-11-15 12:36:34 UTC

Post by Penang
Wonder how a 3D Mandelbrot looks like?
http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

http://www.bugman123.com/Hypercomplex/index.html
I don't believe these satisfy the self-similar aspect of the Mandlebrot
set. For that matter, does such exist in nature?

They are most definitely self-similar but they do appear to be missing
certain aspects of the classic Mandelbrot such as the antennae.
To easily see the self-similarity they exhibit just zoom into say the
degree 8 or 9 version and you'll immediately find that the brocolli
"buds" extend to all depths in the normal self-similar manner. For
example here's the deepest zoom I've done so far (about as far as you
can go without extending precision beyond "double"):
http://www.fractalforums.com/gallery/?sa=view;id=1043

Roger Bagula

2009-11-15 14:46:17 UTC

Post by David Makin

Post by Penang
Wonder how a 3D Mandelbrot looks like?
http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

http://www.bugman123.com/Hypercomplex/index.html
I don't believe these satisfy the self-similar aspect of the Mandlebrot
set. For that matter, does such exist in nature?

They are most definitely self-similar but they do appear to be missing
certain aspects of the classic Mandelbrot such as the antennae.
To easily see the self-similarity they exhibit just zoom into say the
degree 8 or 9 version and you'll immediately find that the brocolli
"buds" extend to all depths in the normal self-similar manner. For
example here's the deepest zoom I've done so far (about as far as you
can go without extending precision beyond "double"):http://www.fractalforums.com/gallery/?sa=view;id=1043

One of the problems with the cubic Julia version of the 2d Mandelbrot
set
is the lack of the rational antenna that characterize the
quadratic 2d Mandelbrot set.
These antenna seem to be based on mode locking to rational Farey tree
angles.
The broccoli shape of this new 3d Mandelbrot is kind of pretty,
but reminds one of a standing wave type of 3d surface
more than a Mandelbrot set.
I don't think the question is through yet/solved.

But I think the efforts are very pretty fractals.

A symmetrical Mandelbrot is obtained in 2d that retains the antenna
feature:
x'=2*x*y-x^2+x0;
y'=2*x*y-y^2+y0
http://www.flickr.com/photos/fractalmusic/4106023768/
This suggests that a symmetrical version something like:
x'=2*t*x - x^2 +x0
y'=2*t*y - y^2 +y0
z'=2*t*z - z^2 +z0
Where t symmetrically cycles through {x,y,z} as:
x'=2*y*x - x^2 +x0
y'=2*z*y - y^2 +y0
z'=2*x*z - z^2 +z0
There is no guarantee that this will
preserve the antenna effect,
but it seems worth a try.

Respectfully, Roger L. Bagula

11759 Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
http://www.google.com/profiles/Roger.Bagula
alternative email: ***@gmail.com

Alan Browne

2009-11-15 19:09:12 UTC

Post by David Makin

Post by Penang
Wonder how a 3D Mandelbrot looks like?
http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

http://www.bugman123.com/Hypercomplex/index.html
I don't believe these satisfy the self-similar aspect of the Mandlebrot
set. For that matter, does such exist in nature?

They are most definitely self-similar but they do appear to be missing
certain aspects of the classic Mandelbrot such as the antennae.
To easily see the self-similarity they exhibit just zoom into say the
degree 8 or 9 version and you'll immediately find that the brocolli
"buds" extend to all depths in the normal self-similar manner. For
example here's the deepest zoom I've done so far (about as far as you
http://www.fractalforums.com/gallery/?sa=view;id=1043

I'll take your word for it. I would need an app to explore this with
and I don't want to install such. Other fish to fry.

Penang

2009-11-16 06:55:46 UTC

Post by Penang
Wonder how a 3D Mandelbrot looks like?
http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

http://www.bugman123.com/Hypercomplex/index.html
I don't believe these satisfy the self-similar aspect of the Mandlebrot
set. For that matter, does such exist in nature?

The other day I watch an old episode of Discovery, where they talk
about the Sun (Sun spots and all that).

The more I look at the waves and bursts from the Sun, the more they
look like the 3D Mandelbrots.

Sjouke Burry

2009-11-15 01:19:58 UTC

Post by Penang
Wonder how a 3D Mandelbrot looks like?

No, I know!!

Dave

2009-11-15 17:53:55 UTC

On Sun, 15 Nov 2009 02:19:58 +0100, Sjouke Burry

Post by Penang
Wonder how a 3D Mandelbrot looks like?

No, I know!!

or
Now, I know!!

Sjouke Burry

2009-11-15 18:10:57 UTC

Post by Dave
On Sun, 15 Nov 2009 02:19:58 +0100, Sjouke Burry

Post by Penang
Wonder how a 3D Mandelbrot looks like?

No, I know!!

or
Now, I know!!

Now,now, it was really NO.

Henk de Jong

2009-11-15 20:06:18 UTC

Post by Penang
Wonder how a 3D Mandelbrot looks like?

No, I know!!

Still computing Mandelbrot graphics on an Acorn computer? ;-)

--
Met vriendelijke groet,
Henk de Jong
The Netherlands

http://www.hsdejong.nl
Nepal and Myanmar (Burma) - Photo Galleries

Sjouke Burry

2009-11-15 20:36:57 UTC

Post by Henk de Jong

Post by Penang
Wonder how a 3D Mandelbrot looks like?

No, I know!!

Still computing Mandelbrot graphics on an Acorn computer? ;-)

I switched to an arc310 and a pentium :)

I did program 2 3d mandelbroot movies on the arc 310

Not for general use, just a binary frame dump and a player
program to view it.

Mohamed Al-Dabbagh

2009-12-04 15:54:31 UTC

Post by Penang
Wonder how a 3D Mandelbrot looks like?
http://www.skytopia.com/project/fractal/mandelbulb.html

Thank you for that post. For the first time I see the rendering of
fractal images. It's just amazing.

Mohamed Al-Dabbagh

Penang

2010-01-17 02:55:06 UTC

Just found couple of stunning pics of the 3D Mandelbulbs

Loading Image...

Loading Image...

http://dspwhite.deviantart.com/art/The-Eternal-Dream-149572608
Loading Image...

Mohamed Al-Dabbagh

2010-02-09 09:31:52 UTC

Post by Penang
Just found couple of stunning pics of the 3D Mandelbulbs
Loading Image...

Wow.. They are really breathtaking. It would be even more amazing to
incorporate these patterns in an animation with a fly-through camera.
It would give impressions of a microscopic treck inside the guts! Yuk!
But that would be wonderfull. I liked the christmas tree very much
with these added lights to it. Soooooo creative. I would call the
garden you show as the MandelBrochli. LOL.
Thank you Penang.

Mohamed Al-Dabbagh
Senior Graphic Designer

Ejay

2010-02-11 04:27:52 UTC

Post by Penang
Just found couple of stunning pics of the 3D Mandelbulbs
http://fc08.deviantart.net/fs70/i/2010/008/2/3/Mandelbulb_Spine_by_ds...http://fc07.deviantart.net/fs51/i/2009/321/0/c/Honeycomb_Heaven_by_ds...http://fc02.deviantart.net/fs50/i/2009/321/9/9/Mandelbulb_Garden_by_d...http://fc01.deviantart.net/fs70/i/2010/007/8/a/The_Mandelbulb_by_dspw...http://fc09.deviantart.net/fs71/f/2010/001/6/b/Mandelbulb_Xmas_Treeho...http://fc07.deviantart.net/fs70/i/2010/008/3/f/Hell_Just_Froze_Over_b...http://dspwhite.deviantart.com/art/The-Eternal-Dream-149572608http://www.skytopia.com/project/fractal/new/full/Power8side-q20b.jpg

Alan Browne

2010-02-11 21:36:45 UTC